List of top Questions asked in MHT CET- 2021

In the arrangement of the capacitors as shown in figure, each capacitor is of $6\ \mu\text{F}$, then equivalent capacity between points A and B is

A perfect gas of volume 10 litre is compressed isothermally to a volume of 1 litre. The rms speed of the molecules will

The relation obeyed by a perfect gas during an adiabatic process is $PV^{3/2} = \text{constant}$. The initial temperature of the gas is $T$. When the gas is compressed to half of its initial volume, the final temperature of the gas is

If $\cos x = \frac{24}{25}$ and $x$ lies in first quadrant, then $\sin \frac{x}{2} + \cos \frac{x}{2} =$

If $\int_2^e \left[ \frac{1}{\log x} - \frac{1}{(\log x)^2} \right] dx = a + \frac{b}{\log 2}$, then

The population of a city increases at a rate proportional to the population at that time. If the population of the city increase from 20 lakhs to 40 lakhs in 30 years, then after another 15 years the population is

Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of 10 will appear is

Let $A=[a, b, c, d], B=[1,2,3]$. Relation $R_1, R_2, R_3, R_4$ are as follows :
$R_1=[(a, 1), (b, 2), (c, 1), (d, 2)]$
$R_2=[(a, 1), (b, 1), (c, 1), (d, 1)]$
$R_3=[(a, 2), (b, 3), (c, 2), (d, 2)]$
$R_4=[(a, 1), (b, 2), (a, 2), (d, 3)]$, then

If $\vec{r} = -4\hat{i} - 6\hat{j} - 2\hat{k}$ is a linear combination of the vectors $\vec{a} = -\hat{i} + 4\hat{j} + 3\hat{k}$ and $\vec{b} = -8\hat{i} - \hat{j} + 3\hat{k}$, then

The joint equation of pair of lines through the origin and making an equilateral triangle with the line $y=3$ is

Negation of $(p \land q) \rightarrow (\sim p \lor r)$ is

If $A^{-1} = \left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$ and $B^{-1} = \left[\begin{array}{cc}1 & 0 \\ -3 & 1\end{array}\right]$, then $(AB)^{-1} =$

If $A^{-1}=\left[\begin{array}{ccc}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 5 & 5\end{array}\right]$, then $A=$

The area bounded by the parabola $y = x^2$ and the line $y = x$ is

If $y = \sin^{-1}\left[\cos \sqrt{\frac{1+x}{2}}\right] + x^x$, then $\frac{dy}{dx}$ at $x=1$ is

If the equation $3x^2 - kxy - 3y^2 = 0$ represents the bisectors of angles between the lines $x^2 - 3xy - 4y^2 = 0$, then value of $k$ is

The general solution of $\left(x \frac{dy}{dx} - y\right) \sin \frac{y}{x} = x^3 e^x$ is

Water is being poured at the rate of $36\ \text{m}^3/\text{min}$ into a cylindrical vessel, whose circular base is of radius $3\ \text{m}$. Then the water level in the cylinder is rising at the rate of

If $y = \sqrt{e^{\sqrt{x}}}$, then $\frac{dy}{dx} =$

If $2 f(x) - 3 f\left(\frac{1}{x}\right) = x$, then $\int_1^e f(x) dx =$

If $f(x) = \frac{4^{x - \pi} + 4^{\pi - x} - 2}{(x - \pi)^2}$, for $x \ne \pi$, is continuous at $x = \pi$, then $f(\pi)$ is

If area of the parallelogram with $\vec{a}$ and $\vec{b}$ as two adjacent sides is 20 square units, then the area of the parallelogram having $3\vec{a}+\vec{b}$ and $2\vec{a}+3\vec{b}$ as two adjacent sides in square units is

The equation of tangent to the circle $x^2+y^2=64$ at the point $P\left(\frac{2\pi}{3}\right)$ is

$\int \operatorname{cosec}(x-a) \operatorname{cosec} x dx = $

The equation of the plane that contains the line of intersection of the planes $x+2y+3z-4=0$ and $2x+y-z+5=0$ and is perpendicular to the plane $5x+3y-6z+8=0$ is